Senior Liberal Democrat peers once critical of the government's NHS bill signalled an end to the parliamentary rebellion as the health secretary, Andrew Lansley, made a key concession on one of their remaining concerns.

In a letter to the Guardian, 32 peers said the time "for declaratory statements is past", as the Department for Health announced it would be accepting a Lib Dem amendment that the secretary of state should remain responsible for health service provision across England.

Malcolm Grant, the government's choice to run the powerful NHS commissioning board, last week outlined "an extraordinary transformation of responsibility" in the health and social care bill, by shifting responsibility for day-to-day running of the health service from ministers to the quango.

But the government said it would accept an amendment. A government source said it felt the secretary of state's role had always been clear, but was happy to make the situation clearer to satisfy the Lib Dems.

The prime minister's official spokesman said: "During the second reading debate, Lord Howe said we are willing to listen to and consider the concerns that have been raised, including making any necessary amendment to put it beyond doubt that the secretary of state remains responsible and accountable for a comprehensive health service."

Lib Dem peers including Shirley Williams, who until recently led the charge against the bill, have now lent their names to the letter urging peers – in particular, on the Labour benches – to accept it.

Their letter nonetheless makes clear how important they regard the climbdown by Lansley over his stated role. "In order to safeguard the NHS, free at the point of need and accessible to all, Liberal Democrat peers are putting forward amendments which require the secretary of state to remain responsible for health services being provided across England," it says.

The bill goes to a Lords committee this week after the second reading, despite an attempted amendment last week by former GP Lord Rea which would have effectively killed it. In that vote, many Lib Dems previously concerned about the NHS bill fell into line with the government after their leader, Nick Clegg, made it clear they had wrung all the major concessions out of the government that they were likely to.

Whereas the Lib Dem peers once lined up alongside Labour, they now criticise the opposition's approach. "The time for declaratory statements is past. Patients who care passionately about the NHS and staff who want to give the best possible service, need certainty about the future of the health service," they say.

"Any politician who plays party political games with the NHS would be open to justified public criticism. So it is now imperative that members of the House of Lords get on with their job of subjecting this bill to detailed, rigorous scrutiny."

Labour shows no sign of letting up. The new shadow health secretary, Andy Burnham, will seek to pin the bill's troubles on the prime minister, dubbing it "Cameron's NHS betrayal" and listing the PM's three "personal pledges" that have been broken. He will say Cameron has failed to meet his promise of a real-terms increase in NHS funding; that he has broken a promised moratorium on hospital reconfigurations; and that he has abandoned a pledge to avoid top-down reorganisations, as the current health bill is just that.

Lansley will also make a speech on the NHS , announcing a tightening of the inspection regime, with 700 new unannounced inspections of hospitals and care homes. The move follows the publication of the results of 100 unannounced hospital inspections, initiated by the Care Quality Commission, which identified serious concerns about treatment of elderly patients.